Principal frequency and existence of solutions for quasilinear elliptic obstacle problems |
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Authors: | JunXia Meng |
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Institution: | Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China |
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Abstract: | In this paper, we are interested in the first eigenvalue of p-Laplacian and the relation between the first eigenvalue and the existence (or nonexistence) of nontrivial (positive) solution for quasilinear elliptic obstacle problems. Utilizing the fact that obstacle problem have consanguineous relations with corresponding equation, we get a simple approach to study the properties of solutions of obstacle problems, such as existence and nonexistence, regularity and stability, etc. In this paper we are mainly concerned with the existence and nonexistence. |
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Keywords: | Quasilinear elliptic obstacle problem Principal frequency Weak solution Critical exponent |
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